Arvanitoyeorgos, A. Einstein equation for an invariant metric on generalized flag manifolds and inner automorphisms. (English) Zbl 0936.53031 Balkan J. Geom. Appl. 3, No. 2, 17-22 (1998). Author’s abstract: “A generalized flag manifold is a homogeneous space \(G/K\) whose isotropy subgroup \(K\) is the centralizer of a torus in \(G\). We show that the Einstein equation for a \(G\)-invariant metric on \(G/K\) is invariant under the group of inner automorphisms of the Lie algebra of \(G\) that preserve the Lie algebra of \(K\) and a fixed Cartan subalgebra of \(K\)”. MSC: 53C30 Differential geometry of homogeneous manifolds 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:invariant metric; Einstein metric; flag manifold; homogeneous space; inner automorphisms PDFBibTeX XMLCite \textit{A. Arvanitoyeorgos}, Balkan J. Geom. Appl. 3, No. 2, 17--22 (1998; Zbl 0936.53031) Full Text: EuDML EMIS